Efficacy of some primary discriminant functions in

Efficacy of some primary discriminant functions in diagnosing planetary gearboxes Anna Bartkowiak1 and Radoslaw Zimroz2 1

2

Wroclaw University, Inst. of Computer Science, 50-383 Wroclaw PL and Wroclaw School of Applied Informatics, 54-239 Wroclaw PL Wroclaw University of Technology, Diagnostics and Vibro-Acoustics Science Laboratory, 50-051 Wroclaw PL and KGHM CUPRUM R&D Center, Mechanical and Electrical Engineering Group, 53-659 Wroclaw PL

Abstract. We consider the efficiency of some primary discriminant functions applied in planetary gearbox diagnostics. Real data for planetary gearboxes mounted in bucket wheel excavators working in field condition are elaborated. The aim is to perform condition monitoring (faulty or healthy) of such devices. The raw recorded data (vibration series emitted by the device) were first segmented and transformed to frequency domain using power spectra densities (PSD). Next, 15 variables denoting amplitudes of derived spectra were extracted. This yielded two data matrices A and B of size 1232 × 15, and 951 × 15, representing the faulty and the healthy device appropriately. The data are non-Gaussian and the covariances in both groups differ significantly. Now, using Fisher’s discriminant criterion and the kernel methodology, we construct from a learning sample (counting only 600 items) a discriminant function able to provide a discriminant score for distinguishing between the healthy and faulty state of a gearbox. The function proved to be very effective: Both for the learning and the testing data samples (600 and 1483 data vectors respectively) we got 100% correct assignments to the ’faulty’ and ’healthy’ class, with a conspicuous margin between the two classes. The results are visualized in a 2D plane. Keywords: condition monitoring, discriminant analysis, healthy state, faulty state, kernels, nonlinearity, gearbox diagnostics